How do you solve x + y = -1 and 6x – 2y = 18?

2 Answers
Mar 5, 2018

Answer:

See a solution process below:

Explanation:

Step 1) Solve the first equation for #x#:

#x + y = -1#

#x + y - color(red)(y) = -1 - color(red)(y)#

#x + 0 = -1 - y#

#x = -1 - y#

Step 2) Substitute #(-1 - y)# for #x# in the second equation and solve for #y#:

#6x - 2y = 18# becomes:

#6(-1 - y) - 2y = 18#

#(6 xx -1) - (6 xx y) - 2y = 18#

#-6 - 6y - 2y = 18#

#-6 + (-6 - 2)y = 18#

#-6 + (-8)y = 18#

#-6 - 8y = 18#

#-6 + color(red)(6) - 8y = 18 + color(red)(6)#

#0 - 8y = 24#

#-8y = 24#

#(-8y)/color(red)(-8) = 24/color(red)(-8)#

#(color(red)(cancel(color(black)(-8)))y)/cancel(color(red)(-8)) = -3#

#y = -3#

Step 3) Substitute #-3# for #y# in the solution to the first equation at the end of Step 1 and calculate #x#:

#x = -1 - y# becomes:

#x = -1 - (-3)#

#x = -1 + 3#

#x = 2#

The Solution Is:

#x = 2# and #y = -3#

or

#(2, -3)#

Mar 5, 2018

Answer:

Solve algebraically or by graphing the equations.

#x = 2#
#y = -3#

Explanation:

  1. #x + y = -1 #
    #6x - 2y = 18#
  2. #6x + 6y = -6#
    #6x - 2y = 18#
    Multiply each side of one or both equations by a constant so that one variable (in this case #x#) in both equations has the same coefficient (in this case #6#).
  3. #6x + 6y = -6#
    #-(6x - 2y = 18)#
    Subtract the second equation from the first using the distributive property #[ a (b + c) = ab + ac]#.
  4. #8y = -24#
    #y = -3#
    Simplify and solve for #y# by dividing both sides by #8#.
  5. #x + (-3) = -1#
    Plug #-3# in for y in one or both equations (the answer should be the same).
  6. #x = 2#
    Solve for #x# (add #3# to both sides).
  7. #x = 2#
    #y = -3#
    State the answer as #x# and #y# values or as a coordinate #(2, -3)# when graphing the equations.